Behind the Pretty Pictures: How to get the most from your Finite - - PowerPoint PPT Presentation

10-Sep-05

How to get the most from your Finite Element Analysis contractors

Behind the Pretty Pictures:

John Davidson – WorleyParsons Services Ltd: Pressure Equipment Group

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Introduction Aims of this presentation:

• To give a general awareness of finite element analysis (FEA) and its

common applications

• Highlight key issues and potential problems in the methods used
• What should be involved in the validation of FEA work?
• What should a good FEA report contain?
• How do you get the most value out of your FEA contractors?

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Introduction My FEA background:

• Pressure equipment (vessels, piping)
• Structural Components (offshore platform

connections, lifting equipment, Bussleton Underwater Observatory)

• Mechanical and thermal, linear and

non-linear, static and transient analyses

• Use of ANSYS, Caesar II, FEPipe, SACS, USFOS, ABAQUS
• On-the-job training with some supplementary external courses.

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Introduction – The Finite Element Method

Developed in the early 1940’s by Richard Courant and Alexander Hrennikoff to solve complex elastic structural analysis problems. They are numerical techniques used for finding approximate solutions of partial differential equations. Development progressed in the middle to late 1950s for airframe and structural analysis through the work of John Argyris and Ray W. Clough in the 1960s for use in civil engineering. By late 1950s, the key concepts of stiffness matrix and element assembly existed essentially in the form used today, and NASA issued request for proposals for the development of the first finite element software NASTRAN in 1965.

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Introduction – Common FEA Today

Structural and thermal problems are the most common use of FEA today:

• Structural analysis calculates the mesh’s

node displacements

• Displacement components interpolated

across elements to calculate a displacement field in the model.

• Displacement fields are differentiated to

find strains.

• Stresses calculated based on strains and

material elasticity.

• Thermal analysis is similar: an interpolated temperature field is differentiated

to find a temperature gradient. Heat flux is calculated based on gradient and material conductivity.

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Introduction – Some key issues

• Significant increase in software accessibility and hardware power has lead to

a surge in the amount of FEA undertaken.

• Increasing costs of materials is raising the importance of design efficiency –

FEA offers potential to improve and iterate design for comparatively low cost.

• FEA being introduced in university courses – is there a danger of being too

software focussed?

• Misconception of FEA as an engineering panacea; the new primary design

tool.

• The pretty pictures are very useful for mollifying upper management

‘The “perform-FEA” syndrome often stems from bureaucratic misunderstanding rather than engineering need for results’

Paul Kurowski – President ACOM Consulting, USA

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Who should be running your FEA?

FEA is an engineering tool and running the analysis is a specific skill:

• Training is required and the opportunity to practice extensively.
• “Garbage in = garbage out” – the black box dilemma
• Some foundation in the theory behind the method as well as sound engineering

judgment in materials and load conditions is needed as a minimum.

• Some software providers are pushing the integration of FEA with CAD –

encouraging the use of designers/draftspeople as FEA operators. This is a potentially dangerous philosophy. Functions such as “Automeshing” still require an experienced eye to confirm suitability.

• An FE analyst needs to decide which features need modelling, how to apply loads

and boundary conditions, what errors are acceptable, and how the results are interpreted against the relevant codes.

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Who should be running your FEA?

Use of recent graduates as FEA operators:

• Computer-savvy, but lack meaningful experience in the fundamentals of good

engineering design. Understanding the FE method is more important than specific software commands, which are easily learned.

• “Unwillingness to ask too many

questions, graduates may withdraw into isolated world of simulation. This is of no benefit to their growth as a good engineer or to the company employing them.”

• A person eager to use newly acquired

skills and lacking a good grasp of FEA is probably the most dangerous user.

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Who should be running your FEA?

NAFEMS (National Agency for Finite Element Methods and Standards ) has released a quality supplement to ISO 9001 titled R0013 – “Finite element analysis in the design and validation of engineering products” Includes recommendations for the level of experience required to complete certain levels of FEA:

Analysis Category Engineering experience Finite-element experience after formal training Relevant FEA jobs performed

• 1. Vital

5 years 6 months 2 X category 1 under supervisory or 5 X category 2 properly assessed

• 2. Important

2 years 2 months 1 X category 1 or 2 under supervision or 3 X category 3 properly assessed

• 3. Advisory

1 year 1 month Relevant benchmarks

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Codes and Standards – Which to Use? Pressure Vessels Previously ASME VIII, Division 2 and AS1210-Supplement 1:1990.

• Almost identical in their guidance for numerical analysis
• Biased towards linear elastic analysis (written before the FEA

software boom) – the “hopper diagram”

• Although simple to analyse, interpretation of stresses requires

experience and good knowledge of differences between primary and secondary, general and local stresses.

• Stress intensity (Max shear stress / Tresca stress theory) compared

against multiples of the material design strength. Max shear stress theory usually more conservative and simpler to calculate.

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Codes and Standards – The ‘Hopper’ Diagram

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Codes and Standards – Which to Use?

Pressure Vessels ASME VIII Div 2 rewritten in 2007

• Very prescriptive section on design-by-analysis (Ch 5)
• Focussed on protection against:
• Plastic collapse
• Buckling
• Local failure
• Failure under cyclical loading
• Specifies methodology for linear (elastic) and non-linear (plastic) analyses –

now uses Von Mises stress rather than stress intensity. AS1210 to be revised later in 2008 (?)

• Some improved guidance on FEA
• New ASME VIII Div 2 methods may be included in later amendments

Pressure Piping AS4041 currently directs users to AS1210 for complex geometries.

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Codes and Standards – Which to Use?

Structural Components Far fewer codes available that give guidance on FEA use. Some European standards (eg BS 7608, DNV-RP-C203) specify methods for extracting suitable stresses from FEA for fatigue assessment. Some analysts use AS3990 (or similar) based on comparing average stress through sections against a proportion of material yield strength. Clients and analysts must consider what form the loads are given in:

• Working Stress design
• Limit State design

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Codes and Standards – Which to Use?

Determination of stress at FE model singularities for strength and fatigue purposes (DNV-RP-C203)

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Material Design Strength Determination of material design strength is one of the key issues in correctly interpreting FEA results (particularly for pressure equipment). Some variation in design strength between AS1210, ASME VIII and ASME B31.3 etc – remember the fundamental intent behind them! AS1210 – ‘f’ is typically lesser of Yield/1.5 and UTS/3.5 (amended from UTS/4 except for flanges).

• Local membrane stresses limited to 1.5*f (Max = 1* yield strength)
• Local primary + secondary stresses limited to 3*f (Max = 2* yield strength).

Care must be taken with standards using different calculations for ‘f’, eg: AS4041 Class 2P (f =0.72*Yield), AS2885 (f = 0.8*Yield)

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Material Design Strength

“Sps , is computed as the larger of the quantities shown below. 1) Three times the average of the S values for the material at the highest and lowest temperatures during the operational cycle. 2) Two times the average of the Sy values for the material at the highest and lowest temperatures during the operational cycle……” – ASME VIII Div 2

CAUTION – Careful consideration

• f the definition of “load cycle” is

required! For steady state conditions (say pressure + external loads at operating temperature) it is more correct to determine the design strength at the

• perating temperature.

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Modelling Techniques – Solids vs Shells

• Consider maximum stress locations
• Bending stresses at repad edges
• Weld geometry, etc…

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Modelling Techniques – Solids vs Shells

Nozzle thickness Shell thickness Shell + repad thickness Neutral Axis

…corresponds with… No bending stress at repad edge accounted for!

Bending stiffness ⍺ (2t)³ Bending stiffness ⍺ 2(t³) Shell + repad? Somewhere in between…

2t t t

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Modelling Techniques – Hexahedra vs Tetrahedra

A second-order hexahedral element A volume built from first-order tetrahedral elements

Three basic approaches to reducing % element error in FEA:

• ‘h’ method: the element order (p) is kept constant, but the mesh is

refined infinitely by making the element size (h) smaller.

• ‘p’ method: the element size (h) is kept constant and the element
• rder (p) is increased.
• ‘h-p’ method: the h is made smaller as the p is increased to create

higher order h elements.

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Modelling Techniques – Hexahedra vs Tetrahedra

510MPa 348MPa

An 8-noded hexahedron formed from five tetrahedrons has greater discretisation error than a single 8- noded “brick” because the five tetrahedrons cannot assume all the displacement fields handled by the 8-noded element. (1st order tetrahedra elements also have constant strain behaviour compared to linear strain behaviour across a 1st order hexahedral element). Element selection can be a matter of preference – but there are some key issues to be aware of.

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Modelling Techniques – Element selection

Model 1 -

• 1st order tetrahedra – constant stress across element
• one element through thickness – cannot represent bending stress
• elements will be highly distorted
• shows a maximum Von Mises stress of 18,000 psi.

From “When Good Engineers Deliver Bad FEA” - by Paul Kurowski – ACOM consulting

The mesh and results from the finite-element analysis of a bracket

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Modelling Techniques – Element selection

Model 2 -

• 2nd order tetrahedra – linear stress across element
• one element through thickness – mesh still too coarse to model stress

concentrations

• some elements will be highly distorted
• shows a maximum Von Mises stress of 32,000 psi.

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Modelling Techniques – Element selection

Model 3 -

• 2nd order tetrahedra, enough elements to model stress distribution reasonably

accurately (good starting point)

• analyst needs to successively refine mesh to check that % error in stress is

within permissible limits (stress will increase with each refinement)

• shows a maximum Von Mises stress of 49,000 psi.

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Modelling Techniques – Element selection

Model 4 -

• Adaptive-order ‘p’ elements – software automatically iterates element order at

each location until a user-specified accuracy is achieved (accuracy based on local strain energy, local displacements or global RMS stress etc)

• Shows a maximum Von Mises stress of 62,000 psi.
• Not all software handles adaptive-order elements.

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Validating third party results

Due to general incompatibility between software packages, it is often difficult to get models validated.

• Not necessarily cost-effective to re-build and re-analyse a model from scratch.
• Some gains are being made in FE software’s ability to export CAD-type geometry

files (.IGES, .SAT) which may be imported into client’s CAD packages to allow geometry checking (and vice-versa for model development….)

• Often have to wait until receipt of final reports to highlight any possible problems

with the analysis and assumptions – by then is it too late?

• Can be totally reliant on contractor’s internal checking procedures

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Validating third party results

As part of the contractor’s checking process, the following should be done:

• Confirmation of use of correct element type (shell vs solid, 1st or 2nd order…)
• Confirmation of use of correct analysis type (linear vs non-linear, small vs large deflection)
• Check of material properties, loads, boundary conditions and sum of reaction forces
• Hand calculation of results away from geometric discontinuities (PD/2t, Roark’s Formulae…)
• Check that stress variation across elements is within acceptable limits (mesh density)

Element Order % Stress Variation across element 10% 1 20% 2 30% >2 40%

• Check that units are consistent
• Check contact (if applicable)
• Check model for “free edges”
• Check for solution convergence

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What should a good FEA report contain?

• Software package and version
• List of assumptions:
• Codes/Standards applied
• Design strengths applied
• Description of failure modes considered
• Material Properties

Longitudinal and circumferential restraint at free end Nozzle loads applied at centre of flange face and transferred to face via rigid constraint equations Symmetry constraints applied on Y-Z plane 14MPa pressure applied to all internal surfaces 0.3MPa pressure applied to bottom surface of upper support plate and top surface of lower support plate

• Plot of model geometry (including list of

thicknesses if shell elements used)

• Plot(s) of FE mesh at critical areas
• Type of elements used (shape and
• rder)
• Plot of applied loads and boundary

conditions (including notation for clarity)

Plot c/o Contract Design and Management Services Pty Ltd

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What should a good FEA report contain?

• Plots of the final deflected shape with

colour contouring

• Key results plots
• Stress / Strain / Temperature etc
• Clearly indicating type of stress (Von

Mises, Tresca…) or strain (‘true’, ‘engineering’…)

Other helpful information:

• Summary of reaction forces at

boundaries.

• Additional hand calculations to verify

results away from discontinuities

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Getting the most value from your contractor

Avoid the “Perform FEA” syndrome..

• Stay involved with the FE contractor during the process
• Develop and agree on a design basis with the key assumptions addressed

(loads, materials, failure criteria, critical regions in the component/assembly…)

• Review preliminary results to ensure that the output is as expected.
• Understand that, what may seem like a “minor” design change at your end,

can be significantly more complex to implement in an existing model.

• Review your contractor’s internal auditing:
• Do they have other analysts with enough experience to independently check the

analysis?

• Do they have an analysis verification checklist?
• Documentation should contain enough information that a third party can replicate

the analysis long after the original author is gone.

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Questions? ….. and the obligatory cartoon

Feel free to contact me at John.Davidson@worleyparsons.com for further discussion.